A general trimming approach to robust cluster Analysis

A general trimming approach to robust cluster Analysis

Luis A. García-Escudero, Alfonso Gordaliza, Carlos Matrán, and Agustin Mayo-Iscar

Source: Ann. Statist. Volume 36, Number 3 (2008), 1324-1345.

Abstract

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion α of contaminating data to guarantee the robustness of the method. As a characteristic feature, restrictions on the ratio between the maximum and the minimum eigenvalues of the groups scatter matrices are introduced. This makes the problem to be well defined and guarantees the consistency of the sample solutions to the population ones.

The method covers a wide range of clustering approaches depending on the strength of the chosen restrictions. Our proposal includes an algorithm for approximately solving the sample problem.

Primary Subjects: 62H3

Secondary Subjects: 62H3

Keywords: Robustness; cluster analysis; trimming; asymptotics; trimmed k-means; EM-algorithm; fast-MCD algorithm; Dykstra’s algorithm

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Permanent link to this document: http://projecteuclid.org/euclid.aos/1211819566
Digital Object Identifier: doi:10.1214/07-AOS515

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